Demand Response Coupled with Dynamic Thermal Rating for Increased Transformer Reserve and Lifetime

Abstract

(1) Background: This paper proposes a strategy coupling Demand Response Program with Dynamic Thermal Rating to ensure a transformer reserve for the load connection. This solution is an alternative to expensive grid reinforcements. (2) Methods: The proposed methodology firstly considers the N-1 mode under strict assumptions on load and ambient temperature and then identifies critical periods of the year when transformer constraints are violated. For each critical period, the integrated management/sizing problem is solved in YALMIP to find the minimal Demand Response needed to ensure a load connection. However, due to the nonlinear thermal model of transformers, the optimization problem becomes intractable at long periods. To overcome this problem, a validated piece-wise linearization is applied here. (3) Results: It is possible to increase reserve margins significantly compared to conventional approaches. These high reserve margins could be achieved for relatively small Demand Response volumes. For instance, a reserve margin of 75% (of transformer nominal rating) can be ensured if only 1% of the annual energy is curtailed. Moreover, the maximal amplitude of Demand Response (in kW) should be activated only 2–3 h during a year. (4) Conclusions: Improvements for combining Demand Response with Dynamic Thermal Rating are suggested. Results could be used to develop consumer connection agreements with variable network access.

Distributed Control of Charging for Electric Vehicle Fleets Under Dynamic Transformer Ratings

“…For case II, the tradeoffs from the objective function imply that any EVs that may be throttled must have a sufficiently high SoC and are not negatively impacted by the transformer's capacity. Together, cases I and II imply that (8e) may not be strictly active, so the temperature state in (9) and the convex relaxation (10) can be removed without affecting the optimal solution. Thus, outside of Theorem 1's conditions, the convex relaxation has no impact on the optimal solution, which ensures that no feasible solution for the relaxed SOCP formulation will lead to overheating of the transformer.…”

“…Corollary 1 (Temperature Limit): For the SOCP, at optimality, k + 1 is the last instance for which (8e) is strictly active, if and only if, k is the largest integer for which (10) is tight.…”

“…To accurately model the transformer hot-spot temperature dynamics, a high-order, nonlinear thermodynamic model, such as the IEEE Standard C57.91-1995 (e.g., Clause 7 and Annex G), is often used [5]. However, low-order predictive transformer models (similar to those used herein) have been a topic of research for many years, including accurate regression-based [6], [7] and machine learning [8], [9] models for online estimation and operation and piecewise linear (PWL) approximations [10] for planning purposes. Some of these models are also capable of adapting to different forced air/direction oil operating modes.…”

Analysis of thermal models to determine the loss of life of mineral oil immersed transformers

“…Firstly, A dynamic thermal model of electrical transformer has been offered by Swift based on the principals of heat transfer theory [14]- [17] after that an improved model has been introduced by Susa by assuming the non-linear thermal oil resistance base on swift's approach. In Susa's model the variations of viscosity with temperature were considered [9].…”

Optimal Ageing Limit of Oil-Immersed Transformers in Flexible Power Systems

“…Briefly, the principle of this algorithm consists in adjusting a transformer load for each value of Tamb until the rated hot spot temperature is reached. This algorithm can be especially useful for long horizons because for long intervals (months and years), the optimization problem may become intractable [12]. Briefly, this happens due to the high time resolution of data required by IEC thermal model.…”